The area of a trapezium is 384 $c m^{2}$ .Its parallel sides are in the ratio 3:5 and the perpendicular distance between them is 12 cm.Find the length of each of the parallel sides.

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Solution

Area of trapezium=384 $c m^{2}$

Perpendicular distance (h)=12 cm

$∴ S u m o f p a r a l l e l s i d e s = \frac{A r e a \times 2}{h e i g h t} = \frac{384 \times 2}{12} = 64 c m R a t i o i n p a r a l l e l s i d e s = 3 : 5 L e t f i r s t s i d e = 3 x t h e n s e c o n d s i d e = 5 x ∴ 3 x + 5 x = 64 c m \Rightarrow 8 x = 64 c m \Rightarrow x = \frac{64}{8} = 8 c m ∴ F i r s t p a r a l l e l s i d e = 8 \times 3 = 24 c m S e c o n d s i d e = 8 \times 5 = 40 c m$

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